Geometric Algorithm for Abelian-Gauge Models

Understand

Motivated by the sign problem in several systems, we have developed a geometric simulation algorithm based on the strong coupling expansion which can be applied to abelian pure gauge models.

• We have studied the algorithm in the U(1) model in 3 and 4 dimensions, and seen that it is practical and is similarly efficient to the standard heat-bath algorithm, but without the ergodicity problems which comes from the presence of vortices.
• We have also applied the algorithm to the Ising gauge model at the critical point, and we find hints of a better asymptotic behaviour of the autocorrelation time, which therefore suggests the possibility of a smaller dynamical critical exponent with respect to the standard heat-bath algorithm.